Kelley said Saturday that doctors took out a couple of "decent-sized" lumps on Thursday after a biopsy before the surgery was inconclusive.
"I still don't know the results of what's in my throat, but it's out, and I'm going to get back to pitching for now," he said. "We'll find out when we find out, but for now, I just want to get back to playing, and physically I feel good, I feel healthy. Arm feels good, body feels good."
The 35-year-old right-hander said he expects to get the results from the latest biopsy early next week.
Kelley, who doesn't use any kind of tobacco, said he noticed the issue early this season. He had the lumps checked this month after they got bigger and bothersome while he tried to sleep.
"The doctors, from their experience and just looking at it and feeling it and all of that stuff, they don't seem to be too concerned yet," Kelley said.
While Kelley talked about being activated from the injured list as early as Sunday, manager Chris Woodward said there were no plans to rush things. The manager wants to make sure Kelley is ready physically and mentally to get back on the mound and mentioned Monday or Tuesday as the earliest possibilities for a return.
Kelley said he threw a bullpen Wednesday before going in for surgery and planned to throw another one Saturday. He is 3-0 with two saves and a 1.29 ERA in 14 appearances in his first season with the Rangers. He last pitched May 4.
Kelley has been on the injured list since May 9, when the Rangers said he had an infection. Kelley said he had the initial biopsy around that time, and doctors used needles to access the affected area.
"That wasn't fun," he said. "They were jabbing needles in there trying to get tissue, and basically they didn't get enough."